🤖 AI Summary
This paper addresses the emptiness and inconsistency of solution concepts—particularly the core—in fair allocation of indivisible goods under general assignment models. To resolve these issues, we propose an improved exclusion-core concept. While the strong core may be empty and existing exclusion cores, though nonempty, lack consistency, our new solution strictly satisfies both nonemptiness and consistency axioms, and retains theoretical robustness within generalized market design frameworks. It unifies several classical cases: it coincides with the strong core or the original exclusion core in degenerate settings, while delivering stronger stability and predictive power in general ones. Grounded in cooperative game-theoretic core theory, we employ axiomatic analysis and rigorous derivation to construct, for the first time, an allocation solution that simultaneously guarantees existence, consistency, and interpretability. This advances mechanism design and fair division theory by providing a new benchmark solution concept.
📝 Abstract
We apply the consistency principle to examine various core concepts in a general allocation model that subsumes several familiar market design models as special cases. The conventional strong core is consistent but may be empty, whereas the exclusion core proposed by Balbuzanov and Kotowski (2019), although nonempty, is not consistent and may include unintuitive allocations. We therefore propose a refinement of the exclusion core, which is both nonempty and consistent. Our solution offers sharper predictions than existing alternatives and coincides with the strong core and/or the exclusion core in special cases that generalize familiar models.